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A181689 Number of maximal self-avoiding walks from NW to SW corners of a 5 X n grid.

%I A181689 #19 Sep 08 2022 08:45:54
%S A181689 1,0,8,0,86,0,948,0,10444,0,115056,0,1267512,0,13963520,0,153828832,0,
%T A181689 1694652176,0,18669100976,0,205667768400,0,2265734756752,0,
%U A181689 24960420526224,0,274975961325264,0,3029267044091408,0,33371858326057936,0,367640393509287824,0,4050102862690348880,0,44617875206245953552,0,491531908055724064720,0,5414951194338345409680,0,59653698888134291413584,0,657173751585588653678864,0,7239741169830151881286864
%N A181689 Number of maximal self-avoiding walks from NW to SW corners of a 5 X n grid.
%C A181689 All even terms are 0.
%H A181689 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,11,0,0,0,2).
%F A181689 G.f.: x*(1 - 3*x^2 - 2*x^4)/(1 - 11*x^2 - 2*x^6).
%F A181689 a(n) = 11*a(n-2) + 2*a(n-6) for n>6. - _Wesley Ivan Hurt_, Apr 10 2016
%p A181689 A181689:=proc(n) option remember:
%p A181689 if n mod 2 = 0 then 0 elif n=1 then 1 elif n=3 then 8 elif n=5 then 86 else 11*a(n-2)+2*a(n-6); fi; end: seq(A181689(n), n=1..50); # _Wesley Ivan Hurt_, Apr 10 2016
%t A181689 CoefficientList[Series[(1 - 3*x^2 - 2*x^4)/(1 - 11*x^2 - 2*x^6), {x, 0, 50}], x] (* _Wesley Ivan Hurt_, Apr 10 2016 *)
%o A181689 (Magma) I:=[1,0,8,0,86,0]; [n le 6 select I[n] else 11*Self(n-2)+2*Self(n-6): n in [1..50]]; // _Wesley Ivan Hurt_, Apr 10 2016
%o A181689 (PARI) x='x+O('x^99); Vec(x*(1-3*x^2-2*x^4)/(1-11*x^2-2*x^6)) \\ _Altug Alkan_, Apr 11 2016
%Y A181689 Row 5 of A271592.
%Y A181689 Cf. A000532, A003778, A006865, A014584, A014585, A181688.
%K A181689 nonn,easy,walk
%O A181689 1,3
%A A181689 _Sean A. Irvine_, Nov 17 2010